论文标题
配置模型网络中边缘和林的统计分析
Statistical analysis of edges and bredges in configuration model networks
论文作者
论文摘要
建（Bridge-Edge）是一个边缘，其删除将将其驻留在两个组件的网络组件中。灌木是脆弱的链接，在网络崩溃过程中起着重要作用，这可能是由节点或链接故障，攻击或流行病引起的。因此，内的丰度和特性会影响网络的弹性。我们介绍了配置模型网络中灌木的统计特性的分析结果。使用基于空腔方法的生成函数方法，我们计算概率$ \ hat p（e \ in {\ rm b}）$，即具有度分布p（k）的配置模型网络中的随机边缘e是一个壮大（b）。我们还计算了随机迫害的最终节点的联合度分布$ \ hat P（k，k'| {\ rm b}）$。我们检查了灌木丛对巨型组件（GC）和网络有限树成分（FC）的不同特性。在有限的组件上，所有边缘都是灌木丛，并且没有学位相关性。我们计算概率$ \ hat p（e \ in {\ rm b} | {\ rm gc}）$，即巨型组件上的随机边缘是迫切的。我们还计算了bredges的最终节点的联合度分配$ \ hat P（k，k'| {\ rm b}，{\ rm gc}）$ and non-end-nod-nod-nod-Nodes $ non-nod-nodes of non-bredge（k，k'| {\ rm nb}）的联合度分布$ \ hat p（k，k，k'| {\ rm nb}）。令人惊讶的是，发现灌木的末端节点的K和K度相关，而NB边缘的最终节点的程度是不相关的。因此，我们得出的结论是，巨型成分上的所有度度相关性都集中在林中。我们计算灌木丛的末端节点的协方差，并表明它是负的，即灌木倾向于将高度节点连接到低度淋巴结。结果的含义是在常见攻击场景和拆除过程的背景下讨论的。
A bredge (bridge-edge) is an edge whose deletion would split the network component on which it resides into two components. Bredges are vulnerable links that play an important role in network collapse processes, which may result from node or link failures, attacks or epidemics. Therefore, the abundance and properties of bredges affect the resilience of the network. We present analytical results for the statistical properties of bredges in configuration model networks. Using a generating function approach based on the cavity method, we calculate the probability $\hat P(e\in{\rm B})$ that a random edge e in a configuration model network with degree distribution P(k) is a bredge (B). We also calculate the joint degree distribution $\hat P(k,k'|{\rm B})$ of the end-nodes of a random bredge. We examine the distinct properties of bredges on the giant component (GC) and on the finite tree components (FC) of the network. On the finite components all the edges are bredges and there are no degree-degree correlations. We calculate the probability $\hat P(e\in{\rm B}|{\rm GC})$ that a random edge on the giant component is a bredge. We also calculate the joint degree distribution $\hat P(k,k'|{\rm B},{\rm GC})$ of the end-nodes of bredges and the joint degree distribution $\hat P(k,k'|{\rm NB},{\rm GC})$ of the end-nodes of non-bredge (NB) edges on the giant component. Surprisingly, it is found that the degrees k and k' of the end-nodes of bredges are correlated, while the degrees of the end-nodes of NB edges are uncorrelated. We thus conclude that all the degree-degree correlations on the giant component are concentrated on the bredges. We calculate the covariance of end-nodes of bredges and show it is negative, namely bredges tend to connect high degree nodes to low degree nodes. The implications of the results are discussed in the context of common attack scenarios and dismantling processes.
